240 LIVE LOAD FOR MAXIMUM CHORD STRESSES. Art. 128. 



The above rule may also be deduced by the following simple 

 analysis. In Fig. 176 (a) consider the chord member C7 3 . Taking 

 the section 3-3, the center of moments will be at d. Consider the 



part to the left of the section as in Fig. 176 (&), and let E t be the 

 reaction due to any load on the right of the panel cd. Since there 

 arc no loads on the part under consideration, and since the mo- 

 ments of Z> 3 and L 3 are each zero, the moment of R^ about d must 

 equal the moment of U 3 about d. Since the former is clockwise, 

 the latter must be anti-clockwise, that is, U s acts in the direction 

 shown which makes it compression. 



In like manner let R 2 be the reaction for any load on the left 

 of the panel cd and it will be the only external force acting on 

 the part to the right of the section as shown in Fig. 176 (c). Since 

 the moment of R 2 about d is counter-clockwise, that of U 3 must 

 be clockwise and U s must act in the direction shown which makes 

 it compression again. It follows that any and all loads produce 

 compression in U 3 , and for a maximum all should act, that is, 

 there should be a full live load. This is true no matter how much 

 shear the chord carries. There can be no reversal of chord 

 stresses and the live and dead load stresses are of the same sign, 

 since both are calculated for full load they are proportional to 

 the loads, and live load chord stresses may be taken from the dead 

 load stresses by means of the slide rule. 



It has been shown that there are vertical and horizontal 

 shearing stresses, and bending stresses in a solid beam; that the 

 vertical shearing stresses resist the shear, the bending stresses 

 resist the bending moment, and the horizontal shearing stresses 

 produce the increment of the bending moment (75). In a Pratt 



